By Joseph H. Silverman
The idea of elliptic curves is exclusive through its lengthy heritage and via the range of the equipment which have been utilized in its learn. This ebook treats the mathematics procedure in its sleek formula, by using simple algebraic quantity concept and algebraic geometry. Following a quick dialogue of the mandatory algebro-geometric effects, the ebook proceeds with an exposition of the geometry and the formal crew of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and worldwide fields. ultimate chapters take care of vital and rational issues, together with Siegels theorem and particular computations for the curve Y = X + DX, whereas 3 appendices finish the full: Elliptic Curves in features 2 and three, workforce Cohomology, and an outline of extra complicated issues.
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